A series of definite integrals involving upper incomplete Gamma functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909784927633408 |
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| author | Barczy, Matyas Mező, István |
| author_facet | Barczy, Matyas Mező, István |
| contents | Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial role. We also give an interesting application of our result, namely, a new summation formula for some derivatives of the Bessel functions of the first kind and the Struve functions with respect to the order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A series of definite integrals involving upper incomplete Gamma functions Barczy, Matyas Mező, István Classical Analysis and ODEs Probability 33B20, 60E05 Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial role. We also give an interesting application of our result, namely, a new summation formula for some derivatives of the Bessel functions of the first kind and the Struve functions with respect to the order. |
| title | A series of definite integrals involving upper incomplete Gamma functions |
| topic | Classical Analysis and ODEs Probability 33B20, 60E05 |
| url | https://arxiv.org/abs/2502.10885 |